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In: Advanced Math

4. Define the width of a rectangle as the longest length of its sides. Given a...

4. Define the width of a rectangle as the longest length of its sides. Given a closed
rectangle A in Rn and a partition P of A, define the mesh of P as the maximum
width of its subrectangles. Prove that a bounded function f : A → R is integrable
on A if and only if, for every > 0, there is a δ > 0 such that U(f, P) − L(f, P) <
for every partition P of mesh < δ.

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Expert Solution

Colby Messinger answered 2 years ago
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